But what if Putin thinks that unless he takes Ukraine, Russia will cease to exist (or Putin will cease to exist). In that scenario, taking Ukraine is an existential goal for Russa, and he will blow up the world unless he wins.
Unfortunately, I think the rational thing to do is to apply increasing pressure to Putin until he either backs down or proves that he is willing to blow up the world over Ukraine. If the latter, then we back down. Of course, the risks of that strategy are all too obvious.